I suggest that possibly when gen 3 comes out somewhere in the region could offer a NPC that could delete pokemon's moves. This may seem to not be wanted very often but I believe this should be added since the pokemon world is suppose to be a replica of Pokemon Go and Pokemon together, please take this under consideration.
The server was meant to be a replica of pokemon go but now it is a mix of pokemon go and original games. Plus deleting moves doesn' make sense when you can buy a tm to replace it or just learn old moves
This could be a good idea if you dont want to use a move and the pokemon has run out of pp in all other moves
Deleting doesn't make much sense if you can just replace them with other moves. The move you don't want can already be removed in the replacing process - its just an extra step with this NPC idea. Keep it simple. Ummmmmm, hit the Pokemon Center? xD